First, this from Paul Dirac 1939 (quote taken from an earlier post by Joselle Kehoe):
"There is no logical reason why the method of mathematical reasoning should make progress in the study of natural phenomena but one has found in practice that it does work and meets with reasonable success. This must be ascribed to some mathematical quality in Nature, a quality which the casual observer of Nature would not suspect, but which nevertheless plays an important role in Nature’s scheme. . . What makes the theory of relativity so acceptable to physicists in spite of its going against the principle of simplicity is its great mathematical beauty… The theory of relativity introduced mathematical beauty to an unprecedented extent into the description of Nature. . . We now see that we have to change the principle of simplicity into a principle of mathematical beauty. The research worker, in his efforts to express the fundamental laws of Nature in mathematical form, should strive mainly for mathematical beauty."
…and then from Joselle herself, in another post:
"If mathematics is, as I tend to see it, the mind itself building structure with the elements of thought, then mathematics’ development is like the development of another sense. It is, after all, the structure we give to any sensory data that creates a meaningful thing perceived. And so it is with mathematics. Mathematics, like story and name, brings meaning, not mechanics, to our experience. It increasingly links what we see to what we think we know, as we try to reconcile our immediate experience with what’s ‘out there.’ The evolution of mathematical concepts allows us to probe deeper and deeper into the universe, as well as into our own nature."